A: The common notation for the "intercept" term of an equation specified as Y = a + bX. Mathematically, the a-intercept term indicates the value of the Y variable when the value of the X variable is equal to zero. Theoretically, the a-intercept is frequently used to indicate exogenous or independent influences on the Y variable, that is, influences that are independent of the X variable. For example, if Y represents consumption and X represents national income, a measures autonomous consumption expenditures.

A measure of the change in aggregate production caused by changes in an autonomous expenditure. The expenditures multiplier is the inverse of one minus the slope of the aggregate expenditures line. The simple expenditures multiplier includes ONLY induced consumption. More complex expenditures multipliers include other induced components. Two related multipliers are the tax multiplier, which measures the change in aggregate production caused by changes in taxes, and the balanced-budget multiplier which measures the change in aggregate production from equal changes in both taxes and government purchases.

The expenditures multiplier is actually a family of multipliers that differ based on which components of the Keynesian model are assumed to be induced by aggregate production and income. The simple expenditures multiplier, as the name suggestions, is the simplest variation and includes only induced consumption. Every other component -- investment expenditures, government purchases, taxes, exports, and imports -- are assumed to be autonomous.

More complex expenditures multipliers include different combinations of induced components, ranging all of the way up to the "complete" expenditures multiplier that realistically includes all induced components. Induced consumption, investment, and government purchases all increase the value of the expenditures multiplier. Induced taxes and imports both decrease the value of the expenditures multiplier.

The Simple Expenditures Multiplier

The simple expenditures multiplier is the ratio of the change in aggregate production to an autonomous change in an aggregate expenditure when consumption is the only induced expenditure. This multiplier is as simple as it gets while capturing the fundamentals of the multiplier. Autonomous investment triggers the multiplier process and induced consumption provides the cumulatively reinforcing interaction between consumption, aggregate production, factor payments, and income.

If, for example, the MPC is 0.75 (and the MPS is 0.25), then an autonomous $1 trillion change in investment expenditures results in a change in aggregate production of $4 trillion.

While the simple expenditures multiplier can be derived from the basic two-sector Keynesian multiplier, it also works for models with more sectors, as long as consumption is the only induced expenditure. If, for example, autonomous government purchases change by $1 trillion, then the change in aggregate production is $4 trillion, the same as with a $1 trillion change in investment expenditures. Moreover, the same change in aggregate production is realized if autonomous exports or consumption expenditures change by $1 trillion.

More Complex Expenditures Multipliers

The simple expenditures multiplier assumes that consumption is the only induced component. In the real world, however, consumption is not the only induced expenditure. Investment, government purchases, taxes, and net exports (through imports) are also induced. A more complete, more realistic, and more complex multiplier includes induced components.

Here is the formula for just such a multiplier, which can be labeled m[all].

m[all]

=

1{1 - [MPC + MPI + MPG - (MPC x MPT) - MPM]}

This particular multiplier has a number of abbreviations containing the letters "MP." These are the assorted induced components, with "MP" standing for marginal propensity. In fact, the batch of abbreviations within the brackets "[]" is actually the slope of the aggregate expenditures line.

This complex expenditures multiplier can be used to determine the change in aggregate production resulting from a change in any autonomous expenditure, including consumption, investment, government purchases, and net exports.

This particular expenditures multiplier formulation includes all induced components. However, several other expenditures multipliers that include different combinations of these induced components can be identified. One multiplier can include only induced consumption and induced government purchases. Another can include induced consumption, induced investment, and induced imports. The possibilities are almost endless.

Other Multipliers

The expenditures multiplier is one of several Keynesian multipliers. Two other related multipliers are tax multiplier and balanced-budget multiplier.

Tax Multiplier: The tax multiplier measures changes in aggregate production caused by changes in taxes. Like the expenditures multiplier this comes in several varieties, simple and complex, depending on which expenditures and other components are induced by aggregate production and income. It differs from the expenditures multiplier in that aggregate expenditures change by less than the change in taxes.

Balanced-Budget Multiplier: The balanced-budget multiplier measures the combined impact on aggregate production of equal changes in government purchases and taxes. The balanced-budget multiplier has a value equal to one.

Two other multipliers arise from the financial, or money, side of the economy. They are the deposit expansion multiplier and the money multiplier. The deposit expansion multiplier measures the change in bank deposits caused by a change in bank reserves. The money multiplier measures the change in money caused by a change in bank reserves. Both are useful in the analysis of monetary policy.

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